Heat the oven to 200°F. Fit a rack over a baking sheet and put in the oven. Heat 1 Tbsp of the olive oil in a 12-inch skillet over medium-high heat until hot. Add the chilies and cook, stirring until soft, 3 to 4 minutes. Add the squash, season with salt and pepper, and cook, stirring until the squash softens and starts to brown, 3 to 4 minutes. Stir in the corn and chipotle powder and cook another 2 minutes. Spoon into a bowl, let cool for a few minutes, and fold in the tomato, cilantro, and lime juice. Set aside ¾ cup of the mixture.

Lay several layers of paper towel on a work surface. Wipe out the skillet, put it over medium-high heat, and add 1 Tbsp of olive oil. When it’s hot, put one tortilla in the pan. Quickly distribute ½ cup of the cheese evenly over the tortilla and about a quarter of the remaining vegetable mixture over half the tortilla. When the underside of the tortilla is browned, use tongs to fold the cheese-only side over the vegetable side. Lay the quesadilla on the paper towels, blot for a few seconds, and then move it to the rack in the oven to keep warm while you repeat with the remaining olive oil and tortillas. Cut the quesadilla into wedges and serve immediately with the reserved vegetable mixture and sour cream.